Learning probabilistic models of tree edit distance

Abstract

Nowadays, there is a growing interest in machine learning and pattern recognition for tree-structured data. Trees actually provide a suitable structural representation to deal with complex tasks such as web information extraction, RNA secondary structure prediction, computer music, or conversion of semi-structured data (e.g. XML documents). Many applications in these domains require the calculation of similarities over pairs of trees. In this context, the tree edit distance (ED) has been subject of investigations for many years in order to improve its computational efficiency. However, used in its classical form, the tree ED needs a priori fixed edit costs which are often difficult to tune, that leaves little room for tackling complex problems. In this paper, to overcome this drawback, we focus on the automatic learning of a non parametric stochastic tree ED. More precisely, we are interested in two kinds of probabilistic approaches. The first one builds a generative model of the tree ED from a joint distribution over the edit operations, while the second works from a conditional distribution providing then a discriminative model. To tackle these tasks, we present an adaptation of the Expectation-Maximization algorithm for learning these distributions over the primitive edit costs. Two experiments are conducted. The first is achieved on artificial data and confirms the interest to learn a tree ED rather than a priori imposing edit costs; The second is applied to a pattern recognition task aiming to classify handwritten digits.⋆ This work is part of the ongoing ARA Marmota research project.Email addresses: marc.bernard@univ-st-etienne.fr (Marc Bernard), laurent.boyer@univ-st-etienne.fr (Laurent Boyer), amaury.habrard@lif.univ-mrs.fr (Amaury Habrard), marc.sebban@univ-st-etienne.fr (Marc Sebban). Preprint submitted to Elsevier 30 October 2007A c c e p t e d m a n u s c r i p t

Efficient Adaptation of Structure Metrics in Prototype-Based Classification

“…. , F} represents a difference coding of successive positions, where upper and lower case letters mark positive and negative changes respectively, and "=" means no change 1 . From the database, we use a common benchmark set for binary classification, containing class 4 and 5, with 200 sequences each (N = 400).…”

“…(Note, that symbols f, F did not occur in the data and were thus not considered.) 1 For details, see http://algoval.essex.ac.uk/data/sequence/copchrom/ Table 1: Runtimes (in minutes) to calculate the alignment derivative for all pairs of random stringsā i ∈ Σ L , i ∈ {1 . .…”

“…In bioinformatics, these can be inferred from evolutionary models, but in general their choice is based on a-priori assumptions about the domain or data space [17]. A few promising approaches how to infer scores from exemplary alignments have been proposed [5,18,1,2]. One approach proposes to adapt scores for a discriminative classification task in conjunction with RGLVQ training, leading to first promising results [12].…”

SEDiL: Software for Edit Distance Learning

“…This joint work has lead to publications in the previous conferences ECML'06 [7] and ECML'07 [4], and in Pattern Recognition [3,8]. This research has also received funding from the RedEx PASCAL in the form of a pump-priming project in 2007.…”

“…However, in many real world applications, such a strategy clearly appears insufficient. To overcome this drawback and to capture background knowledge, supervised learning has been used during the last few years for learning the parameters of edit distances [1,2,3,4,7,8,9], often by maximizing the likelihood of a learning set. The learned models usually take the form of state machines such as stochastic transducers or probabilistic automata.…”